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subdirect product of groups (Definition)

Let $(G_i)_{i\in I}$ be a family of groups. A subgroup $H$ of the direct product $\prod_{i\in I}G_i$ is said to be a subdirect product (or subcartesian product) of $(G_i)_{i\in I}$ if $\pi_i(H)=G_i$ for each $i\in I$, where $\pi_i\colon\prod_{i\in I}G_i\to G_i$ is the $i$-th projection map.



"subdirect product of groups" is owned by yark.
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See Also: residually $\mathfrak{X}$, direct products of groups

Other names:  subdirect product, subcartesian product, subcartesian product of groups
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Cross-references: projection map, groups
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This is version 4 of subdirect product of groups, born on 2004-12-13, modified 2006-09-16.
Object id is 6571, canonical name is SubdirectProductOfGroups.
Accessed 2242 times total.

Classification:
AMS MSC: 20E26 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Residual properties and generalizations)
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